A board has 16 squares arranged in a 4 times | vedclass

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Question

(A) The total number of ways to select any two squares from $16$ is given by $^{16}C_2 = \frac{16 	imes 15}{2} = 120$.Two squares have a common side

Vedclass · Accepted Answer

$\frac{4}{5}$

Vedclass · Answer

(A) The total number of ways to select any two squares from $16$ is given by $^{16}C_2 = \frac{16 	imes 15}{2} = 120$.Two squares have a common side if they are adjacent horizontally or vertically.In a $4 	imes 4$ grid,the number of horizontal adjacent pairs is $4 	imes 3 = 12$.The number of vertical adjacent pairs is $4 	imes 3 = 12$.Total number of pairs with a common side = $12 + 12 = 24$.The probability that two chosen squares have a common side is $P(	ext{common side}) = \frac{24}{120} = \frac{1}{5}$.The probability that they have no side in common is $1 - P(	ext{common side}) = 1 - \frac{1}{5} = \frac{4}{5}$.

$A$ board has $16$ squares arranged in a $4 \times 4$ grid. Out of these $16$ squares,two squares are chosen at random. The probability that they have no side in common is:

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